## Certain components of Springer fibers and associated cycles for discrete series representations of $SU(p,q)$

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- by L. Barchini and R. Zierau; \\with an appendix by Peter E. Trapa
- Represent. Theory
**12**(2008), 403-434 - DOI: https://doi.org/10.1090/S1088-4165-08-00311-7
- Published electronically: October 30, 2008
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## Abstract:

An explicit geometric description of certain components of Springer fibers for $SL(n,C)$ s given in this article. These components are associated to closed $S(GL(p)\times GL(q))$-orbits in the flag variety. The geometric results are used to compute the associated cycles of the discrete series representations of $SU(p,q)$. A discussion of an alternative, and more general, computation of associated cycles is given in the appendix.## References

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## Bibliographic Information

**L. Barchini**- Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
- Email: leticia@math.okstate.edu
**R. Zierau**- Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
- Email: zierau@math.okstate.edu
**Peter E. Trapa**- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- Email: ptrapa@math.utah.edu
- Received by editor(s): April 5, 2008
- Received by editor(s) in revised form: February 2, 2008
- Published electronically: October 30, 2008
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**12**(2008), 403-434 - MSC (2000): Primary 20G20, 22E46
- DOI: https://doi.org/10.1090/S1088-4165-08-00311-7
- MathSciNet review: 2461236